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Biophotonics IW. Petrich

Slides of lecture #11 January 15th , 2018

http://www.kip.uni-heidelberg.de/biophotonik/teaching

• Lecture „Biophotonics I“ will be credited with 2 CP subject to

successfully passing the exam

• There will be a written exam („Klausur“) on February 5th 2018

• registration: https://uebungen.physik.uni-heidelberg.de/v/831

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Biophotonics ISUMMARY of lecture#10 (18.12.2017)

II.2. Light scattering at

multiple particles

II.2.2 Boltzman transport equation (radiative transport equation, RTE)

change in

radianceoriginal beam

divergence

total loss(abs.and scatt.) scattering back into prop. direction source of

radiance

Note: coherence, polarisation and

non-linearities are neglected

II.2.1 Scattering in highly dilute media

fluence rate current densityfluence2

Remarks on Rayleigh scattering:

• IS~a6 largest particles vastly

„outperform“ small particles

• IS~-4 blue light scattered much

more than red light

• polarisation dependence:

• Rayleigh formula remains valid for

non-spherical particles

• extension to

Rayleigh-Gans-Debye theory

iS II 2|| cos~

iS II ~

11mkd

2

2

cos1

cos1

P

Example: static light scattering

Prof. Dr. Petrich Biophotonics I (WS 2017/18)

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Biophotonics III.3 Mie scattering in tissue

Wavelength dependence of scattering for 3 different particles sizes (fv=0.001)

(http://omlc.ogi.edu/classroom/ece532/class3/mie.html

Prof. Dr. Petrich Biophotonics I (WS 2017/18) 3

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Biophotonics III.3 Mie scattering in tissue

Wavelength dependence of scattering for 3 different particles sizes (fv=0.001)

(http://omlc.ogi.edu/classroom/ece532/class3/mie.htmlProf. Dr. Petrich Biophotonics I (WS 2017/18) 4

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Biophotonics III.3 light scattering in tissue

0,5 1,0 1,5 2,01E-4

1E-3

0,01

0,1

1

10

100

1000

10000

Haut

Absorptionskoeffizient von Wasser

Absorptionskoeffizient von HbO2

Absorptionskoeffizient von Hb

Absorptionskoeffizient der Haut

Streukoeffizient der Haut

Hämoglobin

(

1/c

m)

Wellenlänge (m)

Wasser

30000

Wellenzahl (cm-1)

500010000

0,3

Wasser

Blut

Haut

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Biophotonics III.3 light scattering in tissue: absorption & scattering in blood

D. F

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Biophotonics III.3 light scattering in tissue

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Biophotonics III.3 light scattering in tissue

htt

p:/

/om

lc.o

gi.edu

/cla

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Mie scattering

from 2.8 µm diam. , cylindrical collagen fiber bundles

np=1.46, nmed=1.35, fv=0.21

Rayleigh contribution

50 nm spheres mimicing ultrastructure in collagen fibrils

np=1.50, nmed=1.35, fv=0.21

full Mie

theory

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Biophotonics III.3 examples

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Biophotonics III.3 examples

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Biophotonics III.3.4 (b) Monte-Carlo Methods

Diffuse reflectance vs. radius from the photon source for an

isotropic point source as characterized by the solution to

the RTE (blue) and a Monte Carlo simulation (red).

Figures from: www.en.wikipedia.orgProf. Dr. Petrich Biophotonics I (WS 2017/18) 11